Spectrum of linearized operator at ground states of a system of Klein-Gordon equations

Yan Cui; Bo Xia; Kai Yang

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arXiv · 2304.09708

Spectrum of linearized operator at ground states of a system of Klein-Gordon equations

Yan Cui·Bo Xia·Kai Yang

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Abstract

Previously, the existence of ground state solutions of a family of systems of Klein-Gordon equations has been widely studied. In this article, we will study the linearized operator at the ground state and give a complete description of the spectrum for this operator in the radial case: the existence of a unique negative eigenvalue, no resonance at '1'(the bottom of the essential spectrum), no embedded eigenvalue in the essential spectrum and the spectral gap property (i.e., there is no eigenvalue in the interval (0,1]).

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Yan Cui, Bo Xia, Kai Yang. 2023-04-19. Spectrum of linearized operator at ground states of a system of Klein-Gordon equations. https://arxiv.org/abs/2304.09708

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